AP PHYSICS C Worksheet #13 Free-Body Diagrams Applications of Newton’s Laws 1. To compensate for a distinct lack of personaility, Herbert relies on the Grand Entrance technique when he attends parties. His latest plan for appearing at a pool party is to arrive by helicopter and then slide down a nylon rope as the helicopter hovers above poolside. However, as the helicopter approaches its destination, the pilot tells Herbert that the rope will break if the tension exceeds 300 Nt. Herbert, whose mass is 61.2 kg, realizes that the rope won’t hold him unless he slides down with an appropriate acceleration. What must his acceleration be if the rope is to not break and ruin the whole effect? 2. A 2kg picture is hung by two wires of equal length. Each makes an angle Q with the horizontal as shown in the diagram below. (a) Find the general equation for tension T, given Q and weight w for the picture. For what angle is T the least? The greatest? (b) If Q = 30 degrees, what is the tension in the wires? 3. A 65 kg boy weighs himself by standing on a scale mounted on a skateboard that is rolling down an incline as shown in the diagram. Assume there is no friction so that the force exerted by the incline is perpendicular to the incline. What is the reading on the scale if Q = 30? 4. Two climbers on an icy frictionless slope, tied together by a 30 m rope, are in the predicament shown below. At time t = 0, the speed of each is zero, but the top climber Paul (mass 52 kg), has taken one step too many and his friend Matt (mass 74 kg) has dropped his pick. (a) Find the tension in the rope as Paul falls and his speed just before he hits the ground? (b) If Paul unhooks his rope after hitting the ground, find Jay’s speed as he hits the ground. 5. A 2 kg block hangs from a spring balance calibrated in newtons that is attached to the ceiling of an elevator. What does the balance read when (a) the elevator is moving up with a constant velocity of 30 m/sec? (b) the elevator is moving down with a constant velocity of 30 m/sec? (c) the elevator is ascending at 20 m/sec and gaining speed at a rate of 10 m/sec2? From t = 0 to t = 2 sec, the elevator moves upward at 10 m/sec. Its velocity is then reduced uniformly to zero in the next 2 sec so that it is at rest at t = 4 sec. Describe the reading on the balance during the interval 0 < t < 4 sec. 6. Find the force exerted by the Atwood’s machine on the hanger to which the pulley is attached while the blocks accelerate. Neglect the mass of the pulley.
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